Related papers: On different types of stability for linear delay d…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
In this paper, we study asymptotic stability of the zero solution of a class of differential systems governed by a scalar differential inequality with time-varying structures and delays. We establish a new generalized Halanay inequality for…
In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…
In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
For the delay differential equations $$ \ddot{x}(t) +a(t)\dot{x}(g(t))+b(t)x(h(t))=0, g(t)\leq t, h(t)\leq t, $$ and $$ \ddot{x}(t) +a(t)\dot{x}(t)+b(t)x(t)+a_1(t)\dot{x}(g(t))+b_1(t)x(h(t))=0 $$ explicit exponential stability conditions…
This paper provides sufficient conditions for global asymptotic stability and global exponential stability, which can be applied to nonlinear, large-scale, uncertain discrete-time systems. The conditions are derived by means of vector…
Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,\tau)||y_\tau||+\int_\tau^t K_1(t,s)||y_s||ds+\int_t^\infty K_2(t,s)||y_s||ds+\rho, \hspace{0.5cm}…
An extensive overview of existing criteria, as well as some new uniform exponential stability tests are included for a scalar delay equation $$ \dot{x}(t)+ \sum_{j=1}^n a_j(t)x(h_j(t))=0. $$ Both cases of continuous and measurable…
Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
We consider a class of scalar delay differential equations with impulses and satisfying an Yorke-type condition, for which some criteria for the global stability of the zero solution are established. Here, the usual requirements about the…
In this paper, we study boundedness, uniform stability and asymptotic stability of a class of nonlinear neutral delay differential equations by using Krasnoselskii's fixed point theorem. The results obtained in this paper extend and improve…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…